Vince worked 528 hours in 11 weeks. At what rate did he work in hours per week?
To find the rate at which Vince worked in hours per week, we need to divide the total number of hours worked by the number of weeks he worked:
Rate = Total hours worked / Number of weeks
Rate = 528 / 11
Rate = 48
Therefore, Vince worked at a rate of 48 hours per week.
Ronald is calculating the time required to fill the swimming pool at school. He found that it takes 14 minutes to fill the swimming pool with 126 gallons of water. At what rate does the swimming pool fill, in gallons per minute?
To find the rate at which the swimming pool fills, we need to divide the number of gallons of water by the time it takes to fill the pool:
Rate = Gallons of water / Time to fill the pool
Rate = 126 / 14
Rate = 9
Therefore, the swimming pool fills at a rate of 9 gallons per minute.
12(-4)
The expression 12(-4) can be simplified using the order of operations, which is a set of rules that dictate the order in which calculations are performed. The order of operations is:
1. Perform operations inside parentheses.
2. Evaluate all powers (exponents).
3. Perform all multiplication and division, from left to right.
4. Perform all addition and subtraction, from left to right.
Following these rules, we can simplify 12(-4) as follows:
12(-4) = -48
Therefore, 12(-4) is equal to -48.
-6(-3)
The expression -6(-3) can be simplified as follows:
-6(-3) = 18
Therefore, -6(-3) is equal to 18.
-16/-4
The expression -16/-4 can be simplified as follows:
-16/-4 = 4
Therefore, -16/-4 is equal to 4.
16/-2 (-9/-3)
To simplify the expression 16/-2 (-9/-3), we need to follow the order of operations, which is a set of rules that dictate the order in which calculations are performed. The order of operations is:
1. Perform operations inside parentheses.
2. Evaluate all powers (exponents).
3. Perform all multiplication and division, from left to right.
4. Perform all addition and subtraction, from left to right.
Following these rules, we can simplify the expression 16/-2 (-9/-3) as follows:
16/-2 (-9/-3) = -8 (3)
Then, we can simplify further:
-8 (3) = -24
Therefore, 16/-2 (-9/-3) simplifies to -24.
There are 4 red cards and 8 black cards in a bag. How likely is it that you will randomly draw a blue card?
There are no blue cards mentioned in the problem, so the probability of drawing a blue card is 0 or impossible.
There are 3 green marbles, 8 red marbles, 8 yellow marbles, and 3 black marbles in a bag. How likely is it that you will draw a red or yellow marble?
The probability of drawing a red or yellow marble can be found by adding the probabilities of drawing a red marble and a yellow marble, since these events are mutually exclusive. The probability of an event is defined as:
Probability = Number of favorable outcomes / Total number of possible outcomes
The total number of marbles in the bag is:
Total number of marbles = 3 + 8 + 8 + 3 = 22
The number of favorable outcomes is the sum of the number of red and yellow marbles in the bag:
Number of favorable outcomes = 8 + 8 = 16
Therefore, the probability of drawing a red or yellow marble is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 16 / 22
Probability = 0.727 (rounded to three decimal places)
Therefore, it is 72.7% likely that you will draw a red or yellow marble from the bag.
A goalie in a soccer game blocked 15 out of 21 shots on goal. What is the experimental probability that he will block the next shot on goal?
bot could you help me on: A goalie in a soccer game blocked 15 out of 21 shots on goal. What is the experimental probability that he will block the next shot on goal?
The experimental probability of the goalie blocking the next shot on goal is the ratio of the number of times the goalie blocked the shot to the total number of shots taken. In this case, the ratio is:
Number of shots blocked / Total shots taken
Substituting the given values, we get:
Experimental probability = 15 / 21
Simplifying the fraction, we get:
Experimental probability = 5 / 7
Therefore, the experimental probability of the goalie blocking the next shot on goal is 5/7 or approximately 0.714 or 71.4%.
Lexie rolls a standard number cube (1-6) and spins a spinner with three equal secions. How many outcomes are possible?
Since there are 6 possible outcomes when rolling a standard number cube and 3 possible outcomes when spinning a spinner with three equal sections, but the outcomes of these events are independent, we can find the total number of outcomes by multiplying the number of outcomes for each event:
Total number of outcomes = Number of outcomes for rolling a number cube * Number of outcomes for spinning a spinner
Total number of outcomes = 6 * 3
Total number of outcomes = 18
Therefore, there are 18 possible outcomes when rolling a standard number cube and spinning a spinner with three equal sections.
There are 10 orange counters and 15 red counters in a bag. What is the probability of picking an orange counter from the bag?
The probability of picking an orange counter from the bag can be found using the following formula:
Probability of an event = Number of favorable outcomes / Total number of possible outcomes
In this case, the total number of counters in the bag is 10 + 15 = 25. The number of favorable outcomes is the number of orange counters, which is 10.
Then, we can find the probability of picking an orange counter as:
Probability of picking an orange counter = Number of favorable outcomes / Total number of possible outcomes
Probability of picking an orange counter = 10 / 25
Probability of picking an orange counter = 0.4
Therefore, the probability of picking an orange counter from the bag is 0.4 or 40%.
During his first 20 picks from a back og marbles, Kyle chose 8 yellow marbles, 3 green marbles, and 9 blue marbles. Each time he replaces the marbles before selecting another. Which percent is closest to the experimental probability that Kyle will choose a green marble on his next pick?
The experimental probability of Kyle choosing a green marble on his next pick is the ratio of the number of times he chose a green marble to the total number of picks he made. In this case, Kyle picked a total of 20 marbles and chose 3 green marbles, so the experimental probability of him choosing a green marble on his next pick is:
Experimental probability = Number of green marbles / Total number of picks
Experimental probability = 3 / 20
Multiplying this fraction by 100% gives:
Experimental probability = 3 / 20 * 100%
Experimental probability = 15%
Therefore, the percent closest to the experimental probability that Kyle will choose a green marble on his next pick is 15%.
The S & S Restaurant offeres chicken soup, vegetable soup, and onion soup, along with seven choices of sandwiches. How many different spup & sandwich combinations could you order?
To calculate the total number of soup and sandwich combinations that can be ordered, we multiply the number of soup options by the number of sandwich options.
The number of soup options is 3 (chicken soup, vegetable soup, and onion soup).
The number of sandwich options is 7.
Therefore, the total number of soup and sandwich combinations that can be ordered is:
3 x 7 = 21
Therefore, there are 21 different soup and sandwich combinations that can be ordered.
A coin is thrown 3 times. What is the probability that at least one head is obtained?
To find the probability of getting at least one head in three coin tosses, we need to calculate the probability of getting no heads at all and then subtract that from 1 (the probability of getting at least one head).
The probability of getting no heads in three coin tosses is given by:
(1/2) x (1/2) x (1/2) = 1/8
Therefore, the probability of getting at least one head in three coin tosses is:
1 - 1/8 = 7/8
So, the probability of getting at least one head in three coin tosses is 7/8 or approximately 0.875 or 87.5%.
Gustavo wants to buy more than two sandwiches at the city fair. There are three sandwich stands, and each is offering a different deal.
Benny's Sandwiches 8 sandwiches for $10.00
ABC Sandwiches, Inc. 4 sandwiches for $6.00
Sandwich Hut 1 sandwich for $2.00 *Buy 1, get 1 Free*
Which sandwich stand has the best deal for sandwiches?
To compare the deals for sandwiches, we can find the price per sandwich for each deal.
For Benny's Sandwiches, the price per sandwich is:
Price per sandwich = Total price / Number of sandwiches
Price per sandwich = $10.00 / 8 sandwiches
Price per sandwich = $1.25
For ABC Sandwiches, Inc., the price per sandwich is:
Price per sandwich = Total price / Number of sandwiches
Price per sandwich = $6.00 / 4 sandwiches
Price per sandwich = $1.50
For Sandwich Hut, the price per sandwich is:
Price per sandwich = Total price / Number of sandwiches
Since you get one sandwich free for each sandwich you buy, the effective price per sandwich is half of the listed price:
Price per sandwich = $2.00 / 2 sandwiches
Price per sandwich = $1.00
Therefore, Sandwich Hut has the best deal for sandwiches, with a price of $1.00 per sandwich.
Carmen ran 2 laps around the track in 6 minutes. What are the unit rates in laps per minute and minutes per lap?
A.
3 laps per minute and of a minute per lap
B.
of a lap per minute and of a minute per lap
C.
3 laps per minute and 3 minutes per lap
D.
of a lap per minute and 3 minutes per lap
To find the unit rates of laps per minute and minutes per lap, we need to divide the number of laps by the number of minutes and the number of minutes by the number of laps, respectively.
Laps per minute = Number of laps / Number of minutes
Laps per minute = 2 / 6
Laps per minute = 1/3 or 0.333 laps per minute
Minutes per lap = Number of minutes / Number of laps
Minutes per lap = 6 / 2
Minutes per lap = 3 minutes per lap
Therefore, the unit rates are:
- Laps per minute: 1/3 or 0.333 laps per minute
- Minutes per lap: 3 minutes per lap
So, the answer is D. of a lap per minute and 3 minutes per lap.
A car wash detailed 180 cars in 5 hours. At what rate did the car wash detail cars in cars per hour?
A.
34 cars per hour
B.
36 cars per hour
C.
35 cars per hour
D.
37 cars per hour
To find the rate of detailing cars in cars per hour, we need to divide the total number of cars detailed by the number of hours it took to detail them:
Rate = Total number of cars / Number of hours
Rate = 180 / 5
Rate = 36
Therefore, the car wash detailed cars at a rate of 36 cars per hour, and the answer is B.
Jaime wants to know how fast she can type, so she times herself as she types a paper. The paper has 396 words in it, and Jaime types it in 12 minutes. What is her typing rate, in words per minute?
A.
36 words per minute
B.
33 words per minute
C.
34 words per minute
D.
32 words per minute
To find Jaime's typing rate in words per minute, we need to divide the total number of words by the time it took her to type them:
Rate = Total number of words / Time
Rate = 396 / 12
Rate = 33
Therefore, Jaime's typing rate is 33 words per minute, and the answer is B.
Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks 133 times in 7 minutes. What is her blinking rate, in blinks per minute?
A.
33 blinks per minute
B.
19 blinks per minute
C.
10 blinks per minute
D.
20 blinks per minute
To find Jan's blinking rate in blinks per minute, we need to divide the total number of blinks by the time during which those blinks occured:
Rate = Total number of blinks / Time
Rate = 133 / 7
Rate = 19
Therefore, Jan's blinking rate is 19 blinks per minute, and the answer is B.
A video game displays 105 frames in 5 seconds on Penelope's computer. What is the rate in frames per second?
A.
19 frames per second
B.
20 frames per second
C.
22 frames per second
D.
21 frames per second
To find the frame rate in frames per second, we need to divide the total number of frames by the time during which those frames were displayed:
Rate = Total number of frames / Time
Rate = 105 / 5
Rate = 21
Therefore, the frame rate is 21 frames per second, and the answer is D.
Derek wants to practice playing the guitar for 9 hours in 8 days. Which of the following statements match the given ratio for guitar practice?
A.
36 hours in 26 days
B.
27 hours in 24 days
C.
32 hours in 36 days
D.
30 hours in 28 days
bot what is the answer to: Derek wants to practice playing the guitar for 9 hours in 8 days. Which of the following statements match the given ratio for guitar practice?
A.
36 hours in 26 days
B.
27 hours in 24 days
C.
32 hours in 36 days
D.
30 hours in 28 days
We can simplify the given ratio as follows:
Hours per day = Total hours / Total days
Hours per day = 9 / 8
Hours per day = 1.125
Now, we can check each of the answer choices:
A. 36 hours in 26 days yields a ratio of 1.385 hours per day, so it does not match the given ratio for guitar practice.
B. 27 hours in 24 days yields a ratio of 1.125 hours per day, so it matches the given ratio for guitar practice.
C. 32 hours in 36 days yields a ratio of 0.889 hours per day, so it does not match the given ratio for guitar practice.
D. 30 hours in 28 days yields a ratio of 1.071 hours per day, so it does not match the given ratio for guitar practice.
Therefore, only answer choice B, 27 hours in 24 days, matches the given ratio for guitar practice.
Maya is baking cakes for a bake sale. She can bake 3 cakes in 2 hours.
What is Maya's rate in hours per cake?
A.
of an hour per cake
B.
of an hour per cake
C.
of an hour per cake
D.
of an hour per cake
Maya's rate in hours per cake can be found by dividing the time it takes for her to bake a cake by the number of cakes she can bake in that time:
Rate = Time / Number of cakes
Since Maya can bake 3 cakes in 2 hours, her rate is:
Rate = 2 hours / 3 cakes
Simplifying the fraction, we get:
Rate = 2/3 hours per cake
Therefore, Maya's rate in hours per cake is 2/3 hours per cake, and the answer is C.
Paula walked on the treadmill for 12 minutes. The machine told her she had a total of 756 strides. What was her rate in strides per minute?
A.
64 strides per minute
B.
62 strides per minute
C.
61 strides per minute
D.
63 strides per minute
To find Paula's rate in strides per minute, we need to divide the total number of strides by the time during which those strides occured:
Rate = Total number of strides / Time
Rate = 756 / 12
Rate = 63
Therefore, Paula's rate is 63 strides per minute, and the answer is D.
For this question, any answer that is not a whole number should be entered as a fraction in simplest form, using / as the fraction bar, or a decimal rounded to the hundredths place.
Nathan eats the same amount of lunch meat everyday. If Nathan eats 2 pounds of lunch meat in 8 days, he eats
pound(s) of lunch meat per day.
To find the amount of lunch meat Nathan eats per day, we need to divide the total amount of lunch meat by the number of days:
Amount of lunch meat per day = Total amount of lunch meat / Number of days
Amount of lunch meat per day = 2 pounds / 8 days
Simplifying the fraction, we get:
Amount of lunch meat per day = 1/4 pounds per day
Therefore, Nathan eats 1/4 pound or 0.25 pounds of lunch meat per day.